Limitations of the Lipschitz constant as a defense against adversarial examples

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz constant may indeed enable adversarially robust neural networks. However, the methods currently employed for computing it suffer from theoretical and practical limitations. We argue that addressing this shortcoming is a promising direction for future research into certified adversarial defenses.